Home-brewing is the art of turning malt-water and hops into beer, but you could also include Wine-making and Mead-making as types of home-brewing. The best way to learn about zymurgy (using yeast to make alcoholic beverages) is to do it yourself and pay observe (and enjoy) the results.
I highly recommend visiting a local homebrew supply store and talking to the people there. They are very knowledgeable and excited about beer and wine. There is probably a homebrew club (if you live in a metro area) that meets monthly and shares beer (hey, free beer!) where you can meet others also.
For personal study, I also highly recommend John Palmer’s online book, “How to Brew”:
http://www.howtobrew.com/